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NASA NTRS2020

Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier–Stokes Equations

In this paper, we extend the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, we utilize a computationally simple and efficient approach based upon using decoupled interpolation operators. The resulting scheme is entropy conservative/stable and elementwise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation con firm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence), which are comparable to those of the original conforming scheme. Simulations of the Taylor{Green vortex at R(e) = 1,600 and turbulent flow past a sphere at R(e(infinity)) = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h=p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme.

Nonconforming interfaces↗
NASA NTRS1987

Prediction of tip vortex self-induced motion parameters in terms of rotor blade loading

The self-induced motion of curved vortex filaments at the tip of a helicopter rotor blade is investigated analytically. The derivation of a method for inviscid roll-up (IRU) is presented in detail, with attention to the cutoff-distance reformulation of the problem, a control-volume analysis of the self-induction properties of the vortex core, the adaptation of the roll-up method of Betz (1932) to IRU in three dimensions, the treatment of linear and elliptic loading, vortices with turbulent central cores, and the effect of cutoff distance on helicopter free-wake computations. Numerical results showing the significant effect of core properties on the geometry of a rotor wake in hover are presented in graphs and briefly characterized.

Bliss, Donald B.↗
NASA NTRS2003

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Pandya, Shishir A.↗
NASA NTRS1993

Application of a Two Camera Video Imaging System to Three-Dimensional Vortex Tracking in the 80- by 120-Foot Wind Tunnel

A description is presented of two enhancements for a two-camera, video imaging system that increase the accuracy and efficiency of the system when applied to the determination of three-dimensional locations of points along a continuous line. These enhancements increase the utility of the system when extracting quantitative data from surface and off-body flow visualizations. The first enhancement utilizes epipolar geometry to resolve the stereo "correspondence" problem. This is the problem of determining, unambiguously, corresponding points in the stereo images of objects that do not have visible reference points. The second enhancement, is a method to automatically identify and trace the core of a vortex in a digital image. This is accomplished by means of an adaptive template matching algorithm. The system was used to determine the trajectory of a vortex generated by the Leading-Edge eXtension (LEX) of a full-scale F/A-18 aircraft tested in the NASA Ames 80- by 120-Foot Wind Tunnel. The system accuracy for resolving the vortex trajectories is estimated to be +/-2 inches over distance of 60 feet. Stereo images of some of the vortex trajectories are presented. The system was also used to determine the point where the LEX vortex "bursts". The vortex burst point locations are compared with those measured in small-scale tests and in flight and found to be in good agreement.

Meyn, Larry A.↗
NASA NTRS1977

Calculation of lateral-directional stability derivatives for wing-body combinations with and without jet-interaction effects

A theoretical method is presented for predicting the lateral-directional stability derivatives of wing-body combinations with or without the blowing jet effect. The fuselage effect is accounted for by the axial distribution of vortex multiplets. Comparison of the predicted results with experiments and other theoretical methods show good agreement for configurations without the blowing jet. More applicable experimental data with blowing jets are needed to establish the accuracy of the theory.

Lan, C. E.↗
NASA NTRS2016

Overview of the NASA Glenn Flux Reconstruction Based High-Order Unstructured Grid Code

A computational fluid dynamics code based on the flux reconstruction (FR) method is currently being developed at NASA Glenn Research Center to ultimately provide a large- eddy simulation capability that is both accurate and efficient for complex aeropropulsion flows. The FR approach offers a simple and efficient method that is easy to implement and accurate to an arbitrary order on common grid cell geometries. The governing compressible Navier-Stokes equations are discretized in time using various explicit Runge-Kutta schemes, with the default being the 3-stage/3rd-order strong stability preserving scheme. The code is written in modern Fortran (i.e., Fortran 2008) and parallelization is attained through MPI for execution on distributed-memory high-performance computing systems. An h- refinement study of the isentropic Euler vortex problem is able to empirically demonstrate the capability of the FR method to achieve super-accuracy for inviscid flows. Additionally, the code is applied to the Taylor-Green vortex problem, performing numerous implicit large-eddy simulations across a range of grid resolutions and solution orders. The solution found by a pseudo-spectral code is commonly used as a reference solution to this problem, and the FR code is able to reproduce this solution using approximately the same grid resolution. Finally, an examination of the code's performance demonstrates good parallel scaling, as well as an implementation of the FR method with a computational cost/degree- of-freedom/time-step that is essentially independent of the solution order of accuracy for structured geometries.

High-Order Methods↗
NASA NTRS2009

Vortical Flow Prediction using an Adaptive Unstructured Grid Method

A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving vortical flow problems. The first test case concerns vortex flow over a simple 65 delta wing with different values of leading-edge radius. Although the geometry is quite simple, it poses a challenging problem for computing vortices originating from blunt leading edges. The second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the wind-tunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.

Pirzadeh, Shahyar Z.↗
NASA NTRS1976

Numerical studies of three-dimensional breakdown in trailing vortex wakes

The development of dangerous vortex wakes trailing between aircraft for appreciable distance downstream, and posing hazards to following aircraft, is calculated using finite-element three-dimensional relaxation methods. Near-wake, middle-wake, and far-wake conditions are delineated. Vortex system finite lifetimes can be calculated with greater facility owing to the inclusion of a self-induction term in the solution dependent upon local curvature and vortex core radius. Looping and convergence phenomena are studied for single vortex pairs, twin pairs, and multiple pairs. Proportions of flap span and wing span are shown to affect the time to convergence of vortex pairs. The self-induction term renders the convergence time of vortices a sensitive function of wavelength. Wakes trailing between wide-body ('Jumbo') aircraft are also examined.

Hackett, J. E.↗
NASA NTRS1981

Aerodynamic features of designed strake-wing configurations

Sixteen analytically and empirically designed strakes have been aerodynamically tested on a common wing-body to determine the longitudinal characteristics of the configurations. These strakes were selected, in general, due to their superior performance in a water-tunnel test. There they exhibited a good correlation between the hypothesized high value of angle of attack for strake vortex breakdown and the high value of leading-edge suction at the strake tip. The lift and pitch data were reasonably well predicted by an extended suction analogy method, and the lift agreement improved with increasing strake area. The strake-vortex-breakdown angle and configuration maximum lift generally increase with increasing strake area and, to some extent, strake tip leading-edge suction value. The best strake configurations all developed about the same maximum area efficiency value despite their differences in size.

Lamar, J. E.↗
NASA NTRS1990

The calculation of rotor/fuselage interaction for two-dimensional bodies

Unsteady rotor wake interactions with the empennage, tail boom, and other aerodynamic surfaces have a significant influence on the aerodynamic performance of the helicopter, ride quality, and vibration. A Computational Fluid Dynamic (CFD) method for computing the aerodynamic interaction between an interacting vortex wake and the viscous flow about arbitrary 2-D bodies was developed to address this helicopter problem. The vorticity and flow field velocities are calculated on a body-fitted computational mesh using an uncoupled iterative solution. The interacting vortex wake is represented by an array of discrete vortices which, in turn, are represented by a finite core model. The evolution of the interacting vortex wake is calculated by Lagrangian techniques. The flow around circular and elliptic cylinders in the absence of an interacting vortex wake was calculated. These results compare very well with other numerical results and with results obtained from experiment and thereby demonstrate the accuracy of the viscous solution. The interaction of a simulated rotor wake with the flow about 2-D bodies, representing cross sections of fuselage components, was calculated to address the vortex interaction problem. The vortex interaction was calculated for the flow about a circular and an elliptic cylinder at 45 and 90 degrees incidence. The results demonstrate the significant variation in lift and drag on the 2-D bodies during the vortex interaction.

Stremel, Paul M.↗
NASA NTRS1990

Transonic blade-vortex interactions noise: A parametric study

Transonic Blade-Vortex Interactions (BVI) are simulated numerically and the noise mechanisms are investigated. The 2-D high frequency transonic small disturbance equation is solved numerically (VTRAN2 code). An Alternating Direction Implicit (ADI) scheme with monotone switches is used; viscous effects are included on the boundary and the vortex is simulated by the cloud-in-cell method. The Kirchoff method is used for the extension of the numerical 2-D near field aerodynamic results to the linear acoustic 3-D far field. The viscous effect (shock/boundary layer interaction) on BVI is investigated. The different types of shock motion are identified and compared. Two important disturbances with different directivity exist in the pressure signal and are believed to be related to the fluctuating lift and drag forces. Noise directivity for different cases is shown. The maximum radiation occurs at an angle between 60 and 90 deg below the horizontal for an airfoil fixed coordinate system and depends on the details of the airfoil shape. Different airfoil shapes are studied and classified according to the BVI noise produced.

Lyrintzis, A. S.↗
NASA NTRS1991

The application of experimental data to blade wake interaction noise prediction

Blade wake interaction noise (BWI) has been defined as the broadband noise generated by the ingestion of turbulent trailing tip vortices by helicopter rotors. This has been shown to be the dominant contributor to the subjectively important part of the acoustic spectrum for the approach stage of a helicopter flyover. A prediction method for BWI noise based on the calculated trailing vortex trajectories has been developed and estimates of the vortex turbulence have been made. These measurements were made on a trailing vortex from a split wing arrangement and did not give the spectrum of the velocity fluctuations. A recent experiment carried out to measure the turbulence associated with a trailing vortex and the application of the results to BWI noise prediction is described.

Glegg, Stewart A. L.↗
NASA NTRS1980

Calculation of two dimensional vortex/surface interference using panel methods

The application of panel methods to the calculation of vortex/surface interference characteristics in two dimensional flow was studied over a range of situations starting with the simple case of a vortex above a plane and proceeding to the case of vortex separation from a prescribed point on a thick section. Low order and high order panel methods were examined, but the main factor influencing the accuracy of the solution was the distance between control stations in relation to the height of the vortex above the surface. Improvements over the basic solutions were demonstrated using a technique based on subpanels and an applied doublet distribution.

Maskew, B.↗
NASA NTRS1974

Aerodynamic influence coefficient method using singularity splines

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Mercer, J. E.↗
NASA NTRS1982

Calculation of vortex flows on complex configurations

The calculation of aerodynamic characteristics of complex configurations having strongly coupled vortex flows is a non-linear problem requiring iterative solution techniques. This paper discusses the use of a low-order panel method as a means of obtaining practical solutions to such problems. The panel method is based on piecewise constant source and doublet quadrilateral panels and uses the internal Dirichlet boundary condition of zero perturbation potential. The problems of predicting vortex/surface interaction and vortex separation are discussed. Some example calculations are included but further test cases have yet to be carried out, in particular for comparisons with experimental data. The problem of convergence on the iterative calculation for the shape of the free vortex sheet is addressed and a preprocessor routine, based on an unsteady, two-dimensional version of the panel method, is put forward as a cost-effective way of generating an initial vortex structure for use as a starting solution for general configurations.

Maskew, B.↗
NASA NTRS1995

Delta wing vortex manipulation using pulsed and steady blowing during ramp pitching

The effectiveness of steady and pulsed blowing as a method of controlling delta wing vortices during ramp pitching has been investigated in flow visualization experiments conducted in a water tunnel. The recessed angled spanwise blowing technique was utilized for vortex manipulation. This technique was implemented on a beveled 60 delta wing using a pair of blowing ports located beneath the vortex core at 40% chord. The flow was injected primarily in the spanwise direction but was also composed of a component normal to the wing surface. The location of vortex burst was measured as a function of blowing intensity and pulsing frequency under static conditions, and the optimum blowing case was applied at three different wing pitching rates. Experimental results have shown that, when the burst location is upstream of the blowing port, pulsed blowing delays vortex breakdown in static and dynamic cases. Dynamic tests verified the existence of a hysteresis effect and demonstrated the improvements offered by pulsed blowing over both steady blowing and no-blowing scenarios. The application of blowing, at the optimum pulsing frequency, made the vortex breakdown location comparable in static and ramp pitch-up conditions.

Moreira, J.↗
NASA NTRS1983

Calculation of potential flow past non-lifting bodies at angle of attack using axial and surface singularity methods

Two different singularity methods have been utilized to calculate the potential flow past a three dimensional non-lifting body. Two separate FORTRAN computer programs have been developed to implement these theoretical models, which will in the future allow inclusion of the fuselage effect in a pair of existing subcritical wing design computer programs. The first method uses higher order axial singularity distributions to model axisymmetric bodies of revolution in an either axial or inclined uniform potential flow. Use of inset of the singularity line away from the body for blunt noses, and cosine-type element distributions have been applied to obtain the optimal results. Excellent agreement to five significant figures with the exact solution pressure coefficient value has been found for a series of ellipsoids at different angles of attack. Solutions obtained for other axisymmetric bodies compare well with available experimental data. The second method utilizes distributions of singularities on the body surface, in the form of a discrete vortex lattice. This program is capable of modeling arbitrary three dimensional non-lifting bodies. Much effort has been devoted to finding the optimal method of calculating the tangential velocity on the body surface, extending techniques previously developed by other workers.

Shu, J. Y.↗